Causation, Relation that holds between two temporally simultaneous or successive events when the first event (the cause) brings about the other (the effect). According to David Hume, when we say of two types of object or event that “X causes Y” (e.g., fire causes smoke), we mean that (i) Xs are “constantly conjoined” with Ys, (ii) Ys follow Xs and not vice versa, and (iii) there is a “necessary connection” between Xs and Ys such that whenever an X occurs, a Y must follow. Unlike the ideas of contiguity and succession, however, the idea of necessary connection is subjective, in the sense that it derives from the act of contemplating objects or events that we have experienced as being constantly conjoined and succeeding one another in a certain order, rather than from any observable properties in the objects or events themselves. This idea is the basis of the classic problem of induction, which Hume formulated. Hume’s definition of causation is an example of a “regularity” analysis. Other types of analysis include counterfactual analysis, manipulation analysis, and probabilistic analysis.

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in logic, a set of ordered pairs, triples, quadruples, and so on. A set of ordered pairs is called a two-place (or dyadic) relation; a set of ordered triples is a three-place (or triadic) relation; and so on. In general, a relation is any set of ordered n-tuples of objects. Important properties of...

problem of justifying the inductive inference from the observed to the unobserved. It was given its classic formulation by the Scottish philosopher David Hume (1711–76), who noted that all such inferences rely, directly or indirectly, on the rationally unfounded premise that the future will...